Solving
Linear Equations
We can use the following procedure to find a solution of a linear equation
in two variables.
Procedure â€”
To Find a Solution of a Linear Equation in Two Variables
Step 1 Choose a value for one of the variables and substitute it in
the equation.
Step 2 Solve the equation for the remaining variable.
Step 3 Write the numbers from Step 1 and Step 2 as an ordered
pair.
Example 1
Find a solution of 2x + y = 7.
Solution
Step 1 Choose a value for one of the variables and substitute it in the
equation.
We may select any real number for
x or y.
Letâ€™s select 3 for x and substitute
it into the equation. 
2x + y = 7
2(3) + y = 7 
Step 2 Solve the equation for the remaining variable.
Simplify . Subtract 6 from both sides. 
6 + y = 7
y = 1 
Step 3 Write the numbers from Step 1 and Step 2 as an ordered pair.
A solution of the equation 2x + y = 7 is (3, 1).
Example 2
Complete the table for the equation 3x + y = 4.
Solution
For each ordered pair, substitute the given value in the equation.
Then solve for the remaining variable.
Let x = 2.
Substitute 2 for x.
Simplify.
Add 6 to both sides. Let y = 8.
Substitute 8 for y.
Add 8 to both sides.
Divide both sides by 3. 
3x + y
3(2) + y
6 + y
y 3x + y 3x +
(8) 3x x 
= 4 = 4
= 4
= 10 = 4 = 4 = 12 = 4 
The completed data table looks like this:
